Let \(\mathcal {P}=\lbrace P_1,\dots ,P_n\rbrace \)  be a set of distinct rational places of \(F\) .
For a special divisor \(G\)  of \(F\)  with \(0<\deg (G)<n\)  and \({\rm supp }(G)\cap \mathcal {P}=\emptyset \) , the algebraic geometry code associated with \(\mathcal {P}\)  and \(G\)  is defined to be
\(\mathcal {C}(\mathcal {P},G):=\lbrace (f(P_1),f(P_2),\dots ,f(P_n)): \; f\in \mathcal {L}(G)\rbrace .\) 
Then \(\mathcal {C}(\mathcal {P},G)\)  is an \([n,k,d]_q\) -linear code with dimension \(k=\ell (G)\)  and minimum distance \(d\geqslant n-\deg (G)\)  from [1]}.
